Digital Artform

Wide-angle lenses are the cause of the distortion. Suppose I want to take a head-and-shoulders photo of someone. I have several choices: I can use a telephoto lens and stand far away so that the 35mm frame is filled by the person. Or I could use a wide-angle lens, but in order to get the same framing that I did with the telephoto lens, I must stand very close to the subject. Try both techniques, and you'll see that the image taken up-close with the wide-angle lens will be distorted.

The analysis in the original post is completely flawed. Obviously if a wide-angle lens is used to capture the river scene, the distortion is not going to be as noticable as with the portrait, since the distance between the lens and the closest object in focus is much larger. The bottom line is that, placed at distances appropriate to achieve the same subject framing, a wide-angle lens of similar quality will display significantly more distortion than the telephoto lens.

Distortion is not a myth, it exists. If I had the effort to prove it to you, I would, but to do so would be a waste of my time.

http://www.dpreview.com/learn/?/Image_Techniques/Barrel_Distortion_Correction_01.htm

You are confusing barrel and pincushion distortion with perspective distortion. Barrel distortions and pincushions are lens defects that TEND TO be associated with certain kinds of lenses. They are not inherent qualities of those lenses.

Allow me to capitalize the key words in the quote the link to which you yourself provided:

"TYPICALLY, wide angle lenses TEND TO suffer from barrel distortion and tele lenses from pincushion distortion. Both effects TEND TO be stronger at the extreme ends of zoom lenses, ESPECIALLY on compact cameras."

Barrel distortion is quite real, but it is not a defect shared by every wide angle lens.

As for the portrait example you cite, it is the DISTANCE TO THE SUBJECT which cause the perspective distortion (or lack thereof), not the lens focal length.

You were warming up to the idea yourself when you said, "Obviously if a wide-angle lens is used to capture the river scene, the distortion is not going to be as noticable as with the portrait, since the distance between the lens and the closest object in focus is much larger."

Look at it this way:

Let's say my nose juts an inch from my face. If you photograph me from 100 inches away, my nose is only 1% closer to the camera than my face is. If you photograph me from 5 inches away, my nose is a whopping 20% closer to the camera than is the rest of my face. You are going to need a reducing lens (a/k/a a wide angle lens) to frame me nicely since I'm so close. My nose will look disproportionally large because it is disproportionally close, not because of the lens. All the wide angle or telephoto lens would do is crop me tighter or looser.

Please do take a look at my pre-blog page on lenses:
http://www.digitalartform.com/lenses.htm
and scroll down to the part about the cube.

If you have a set of expensive, flat, fixed focal length lenses, set up any experiment you wish. As long as you don't move the camera, you'll find that any image produced by any lens can be nestled into any other image produced by any other lens.

Get close with a wide angle lens. Photograph a highly distorted subject. Make it a geometric subject with lots of reference points, like the mesh of the corner of a shopping cart. Try a longer lens. The subject will be so big it will spill largely out of frame, but (if your lenses are good ones) you will be able to enlarge or reduce one photo so as to exactly line it up on the other -- complicated wire mesh and all.

If you use a zoom lens, you are more likely to experience barrel distortion or pincushioning. Those are unrelated, and quite real, lens defects.

The argument about noses being located at a certain percentage of the distance from the camera is suggestive, but I think it is a bit off the mark. Philip Greenspun's page also has another demonstration which I think much more clearly illustrates the nature of perspective distortion.

Take a picture of a car using a standard lens and using a wide-angle lens (in both cases making sure that the car fills up the entire picture). The wide-angle version looks distorted. Now move your face close (15 cm or so) to the wide-angle photo and look again. The distortion disappears, even though the distance between the camera and the car of course was not changed.

The perspective projection of a camera (both an idealised pin-hole camera and a real one) acts just like the classic renaissance illustration of linear perspective, where one places a plate of glass between the artist and the subject and lets him trace it. Depending on the focal lenght, the photo will cover a greater or smaller field of view of the scene. If the resulting photo is then presented so that it occupies a smaller or larger portion of the viewers field of view than the scene in it represents, the perspective will appear exaggerated or flattened respectively.

Normal 35mm objects happen to cover about the same field of view as that taken up by a typically-sized photo print viewed from normal viewing distance. If you were to print the same photo poster-sized and view it from up close, the perspective would appear flattned -- you would need to use a wide-angle lens to reproduce the correct perspective.

Sometimes this distortion is desirable, for example when trying to picture a dynamic city-scape, or when taking a portrait. In the latter case, the reason that the flattened photo looks better is probably that when we look at a person's face, our brain automatically compensates for perspective effects and shrinks the nose for us... The picture taken by the telephoto lens is still distorted, however.

Of course, just as you say, there is nothing magical about the _lenses_ that produce this effect; you get exactly the same result by cropping a wide-angle photo.

It sounds as if we essentially agree, but I have to say that to me it's all about relative distances. If the nose example seems wrong, then again I must offer the glass or wireframe cube as an example.

Place a 1-foot cube a mile down the road. The front face of the cube is 5280 feet away, and the back face of the cube is 5281 feet away. They will therefore appear almost identical in size, but tiny because they are so far away. A telephoto lens will "enlarge" the scene and they will still appear almost identical in size, although thanks to the telephoto lens they will also be nicely framed.

Place a 1-foot cube only 1 foot away, and its back face will be 2 feet away -- that is to say it will be twice as far away. The size difference will be dramatic.

Since they are so close, a reducing lens (also known as a wide-angle lens) must be used to nicely frame them.

Quote:
“Telephoto lenses don't "flatten" a scene, they merely crop it tighter. Wide angle lenses don't "distort" a scene, they merely crop it looser.”

The original poster posted an informative and educational fact that telephoto pictures are nested in (cropped out) wide angle pictures. However if I understand the suggestion correctly, I don’t agree that this means the pictures should be called only cropped and not flattened or distorted,

I would rephrase the original quote this way:
“Telephoto lenses "flatten" a scene, because they merely crop it tighter than the human eye normally does. Wide angle lenses "distort" a scene, because they merely crop it looser than the human eye normally does”

When we are talking about distorted or flattened scene in this context we mean perspective. The perspective is a perception that exists in the human mind and devices like cameras are designed to reproduce this perception. We have to agree on what is normal perspective in order to say what is flattened or distorted one. As with anything else that exists in the human mind we can argue what is normal perspective, how subjective it is for each person, and if it is a product of human evolution, but there’s a notion I’ve seen in various sources that 30-35mm lens reproduce perspective closest to the human perception. Wide angle and telephoto lenses produce images which appear distorted to the human eye.

Sorry if my English as a second language fails.

Any projection from 3D into 2D entails some form of distortion.

That which we call "extreme perspective" is caused not be wide angle lenses, but by being close to 3D objects.

That which we call "flat" or "orthographic" perspective is caused by being far away from 3D objects.

Sticking your face into an extreme perspective photo make make you think it "feels" better, but the lines still recede agressively to a vanishing point, and that aggressive recession is a function of proximity of camera to subject, not of lens choice.

One of the most concise lens articles I've seen!

As a pro-photographer, I know that wide-angle lenses distort light. It isn't a myth of any sort. In order to really see the distortion, you have to have a more dynamic subject. Portraits are good examples.

Someone's face, 'cropped in' the same amount with a wide angle as with a telephoto (assuming you can get all of it in focus, which is another debate, and really depends on the lenses you are using, and the format you are shooting), will show a very different amount of distortion and come out a very different photo.

The scene chosen for this example is also relatively flat, try shooting something that comes up right to the camera, then continues out to the horizon.

I've had to correct for distortion enough in commercial and building shots to know it exists. Not all wide-angle lenses are the same either.

An easy case is simply a fisheye lens. It's just a really wide angle lens. If you can prove to me that there is no distortion with a fisheye, then I'll believe you.

Okay, one more time:

The wide angle lens isn't what's distorting the face. Being so close to the subject is what distorts it.

Take the longest lens you have and frame a face. Now photograph it. Now without moving the camera or the subject, re-photograph the face with the widest lens you have (so that the subject is tiny in frame)

Now take the wide angle photo and enlarge the crap out of it. It will be identical in distortion to the photo taken with the long lens. Why? Because the distance from camera to subject was the same in both cases.

***

A fish-eye lens is not "simply" a very wide angle lens. It's a very wide angle lens that ALSO fails to retain rectilinear perspective. I refer you to wikipedia:

http://en.wikipedia.org/wiki/Fisheye_lens

"All ultra-wide angle lenses suffer from some amount of distortion. While this can easily be corrected for moderately wide angles of view, rectilinear ultra-wide angle lenses with angles of view greater than 90 degrees are difficult to design. Fisheye lenses achieve extremely wide angles of view by foregoing a rectilinear image, opting instead for a cylindrical perspective, which gives images a characteristic convex appearance."

***

The distortion that I'm talking about is not barrel distortion, it's perspective distortion.

Place a cone relatively close to the camera. Hang a ball from a thread relatively far from the camera so that it looks as if the ball is balancing on the tip of the cone. Using nothing but lenses, try to disconnect the ball from the cone. It can't be done.

Reading your comment starting "any projection from 3D to 2D entails some form of distortion", I think you somewhat missed the point of what I wrote, so I'll try to be a bit more clear this time. (And long-winded, sorry in advance).

Of course a projection into 2D will be distorting things in the sense that the world isn't actually two-dimensional, so we lose out on something. But this isn't a case of extreme value relativism, or "you know, man, sticking up my face to the picture just makes it feel better for me, like... far out, dude", or "it's all conventions anyway, Chinese ink-drawing in isometric perspective can be a just as valid way of conveying your emotions, not to mention cubism or performance art".

Rather, there is on an important sense linear perspective can give us images that are acurately represent a scene, and the perspective should be judged distorted or not based on that standard.

The thought-experiment goes like this: imagine you are standing looking at a view. Now while you blink, a sneaky (but extremly skilled, and fast-working) artist puts at big paper screen a meter in front of you, and then paints each pixel of it in exactly the colour that the landscape behind it would show, had not your line of sight been blocked by the screen. Ignoring the fact that you have two eyes (imagine being a pirate), you will not notice anything different: your view looks exactly the same. The painting on the screen represents the perspective perfectly, without distortion.

How is this perspective realised in the 2D picture? Basically, things looks smaller the further away they are. Note, however, that shrinking is not linear with distance. A pair of tress spaced 10 meters apart, with the closer tree being 5 meters from the viewer, will be very different in size on the picture. Two trees the same distance apart but 200 meters from the viewer will be almost the same size.

Now step back a meter, so the distance to the screen is 2 meters instead of 1. The screen now occupies a smaller fraction of your field of vision than it did before. A bridge in the picture (and in reality) that used to span 20 degrees now only spans 15 or so. Everything basically looks smaller, which we interpret as being further away. However, the internal size-differences are all wrong! A couple of trees that look as if they are 200 meters apart judging from the apparent size still have an relative size difference as if they were only 100 meters apart. The difference in depth is much too big! The perspective is exaggerated! More to the point, your look at the view is clearly distiguishable from the real-life panorama you saw before, so the picture is objectively not reproducing the perspective faithfully.

The same resoning shows that if we step up so the screen is 0.5 meters away, the picture will look too flat. This is also a form of distortion.

The above thought-experiment again shows that it is only meaningful to talk about perspection distortion in relation to the amount of the viewer's field of view the picture occupies (measured in degrees) compared to the field of view of the scene depicted in it. Each linearly projected image has an "ideal viewing distance". If you view the wide-angle car photo from close up, the perspective is objectively not distorted.

(This is of course where fish-eye lenses differ: they don't project the image according to the "put a screen between the camera and object" metaphore)

I can't tell if we agree or disagree, but here's my response:

First, I'm with you on your thought experiment right up until you talk about stepping back from the screen. I'd prefer you say you shrink or enlarge the screen, not talk about changing distance to the screen. If we keep your idea of stepping back, then the bridge in the picture will look smaller, and the bridge in real life will look smaller, but not to the same amount, as you seem to imply.

Second, by way of a response, I propose a second thought experiment:

Let's say your pirate has a telescope. If he blinks and the world becomes a screen, and then he does the same thing with a telescope, and he takes both screens into a place where artwork can be resized, he can blow one up to fit the other and every aspect of one will perfectly align with every aspect of the other (minus the missing margin around the edges).

I agree with you that there is a perceptual distortion arising from seeing small distant objects filling your field of view (as in the case of a telephoto lens). That's not the distortion I'm talking about. I'm talking about the distortion that makes one of two identical objects seem to tower over the other -- or the front end of a box seem to dwarf the back end of a box. That's a distance-driven distortion, not a lens-driven distortion.

Hm, now we are getting to the point where I can't tell if we are agreeing or not either. :-) I guess what I am mainly reacting against is calling the distortion "distance driven", since it makes it sound as if the perspective in a given picture is objectivly distorted or not; but whether it is distorted or not depends on how big and how far away the picture is when it is presented to the viewer.

Yes, it was perhaps careless to speak about stepping back from the picture -- I imagined being so far away from the (real) bridge that there would be no big difference in perceieved size. Scaling it down was what I had in mind. I completely agree with the thought experiment involving a telescope. Telephoto/wideangle lenses do nothing that can't be reproduced by magnifying and cropping the image.

I'm talking about exactly the distortion you describe, which creates an exaggerated perspective like in a Dali painting. In addition to wide-angle photos, you see exactly the same thing by looking the wrong way through a pair of binoculars. Of course there is the corresponding distortion in the other direction: if you look at a scene through binoculars or a telephoto lens, things will appear packed together along the depth axis and the scene looks flat, for exactly the same reason.

But note that if we took the picture we see from an pair of 8x magnifying binoculars, and made it 8 times smaller, it would nest perfectly into the scene as seen by the naked eye (as you describe in the main article). In other words, just by making the picture 8 times smaller, the unnatural flatness disappears. This is what I mean by saying that the distortions of the perspective in a picture doesn't come from the distance to the objects when the photo was taken, but rather from the size of the print when it was shown to the viewer.

A question to the luminaries (I could probably work it out but my brain hurts!): I'm hoping that there is at least some agreement on the effects in question, that a portrait taken at 1.5m with a 35mm lens on a 28mm (135) camera is going to show a bigger nose relative to a portait taken at 3m with a 135mm lens on the same camera. So my question is, do the effects from these focal lengths bear any geometric relationship to the distance of the lens from the film plane? In other words, if I take a 1950s Rolleiflex or Yashica 6x6 camera (120) with a 35mm insert (Rolleikin, etc.) and use its 80mm lens, do I get less "big nose" on the 35mm film (which is just a crop of the 6x6) than a lens with the equivalent angle of view but which is closer to the film plane, i.e., a 50mm lens used on a 135 camera? And by extension, if I take an old 6x9 camera with a 105mm lens and an even longer distance of lens to film plane, if I take a portrait sufficient to cover the area of a 135 frame (36 x 24mm) do I see the result as if I had used a 105mm on a 135 camera, or a 50mm on a 135 camera? Your comments, please!

Yikes!

I didn't work any of these out, but if we define distortion in a portrait as "big nose effect" then the following, I believe, holds true:

If you can increase the size of the film, but not change the lens, nor the distance from lens to subject, nor the subject, then the new photo on the larger format will have the same "big nose effect" as before, but the subject will be loosely framed with lots of background all around.

If you compensate for the new looseness by moving the camera closer to the subject, then you will (by virtue of the new shorter distance to the subject) increase the "big nose effect."

In standard 35 mm (8-perf) photography, a 50 mm lens is often described as a "normal lens." In the movie industry, where film frames are (generally) confined to a smaller (4-perf) area, a 35 mm lens is often described as a "normal lens."

Thanks Joseph, and quite! It's half the answer, so I probably wasn't clear enough in the question, which is, everything else being constant, what effect does changing the distance from the back of the lens to the film plane have? (I think this distance is called the register, or registration.) If you have a 6x9 camera shooting on 120 film, it uses a 105mm lens to get the same angle of view as a 50mm lens on a 35mm camera, but the register (distance from rear of the lens to the film) is much larger. In the 1950s, your average pro photographer used a 6x6 Rolleiflex with a 75 or 80mm lens, and took portraits. Longer register than 35mm, didn't fill the frame, but surely no big noses?

(continued) Does that mean that a 75mm lens on a 6x6 camera is actually a "portrait lens"? - and that having to have a "portrait lens" on a 35mm camera is only as a result of needing a 50mm lens as standard to obtain a wide enough field of view for such a short register (lens to film plane length)? Or, does it mean that a 75mm lens on a 6x6 camera produces the same amount of "big nose" distortion as a 50mm would on a 35mm camera, which would be the case if the "register" were a proportional factor in the geometry?

To answer my own question, I asked someone else I respect and the answer is as I thought, confirming what was first stated here, that the "big nose" distortion arises only as a function of the distance of subject to lens in relation to the focal length of the lens. There is apparently no relation to the distance from lens back to film plane. Hence, all else being equal, an 80mm lens (for example, as found on a Rolleiflex TLR) will deliver the same image geometrically on the middle 24x36mm section of 120 film frame (58x58mm)as it will on the whole 24x36mm frame of 135 film. Which is what we knew all along - if you go wide, keep your distance!

this is adding to a year old discussion, but just in case some poor unsuspecting soul gets caught up in it in the future...

getting closer to a subject appears to expand space into the distance, getting farther from it appears to compress space.

there is a very clever example of this in
"Photography" by Bruce Warren.
ISBN 0-314-92914-2 (soft)
chapter 4, perspective (p. 73 in this edition)

The subject is on a running track with bleachers in the background. The subject is framed the same in each shot. The lenses used are 24, 50, 100, and 200mm. In the 24mm shot, the sides of the bleachers can be seen, the structure appears smaller and farther away from the subject. The lines of the running track are more spaced out. In the 200mm shot, the bleachers fill the whole background and appear to be just a few feet from the subject. The lines of the running track are very close together.

The important thing to remember is that different lenses can be used to achieve different effects. Experiment with them.